Multiscale methods for elliptic partial differential equations and related applications
Abstract:
Multiscale problems arise in many scientific and engineering disciplines.
A typical example is the modeling of flow in a porous medium containing a
number of low and high permeability embedded in a matrix. Due to the high
degrees of variability and the multiscale nature of formation properties,
not only is a complete analysis of these problems extremely difficult, but
also numerical solvers require an excessive amount of CPU time and
storage.
In this talk, I will introduce multiscale numerical methods for the
elliptic equations. I will review the multiscale finite element method and
related homogenization theorems. My work is focusing on interface and
two-phase flow problems. The model problems we considered are motivated by
the multiscale computations of flow and transport of two-phase flow in
strongly heterogeneous porous media. Although the analysis is carried out
for simplified model problems, it does provide valuable insight in
designing accurate multiscale methods for more realistic applications.
Tea Time: 3:30PM R707